Abstract Rewriting


Title: Abstract Rewriting
Authors: Christian Sternagel and René Thiemann (rene /dot/ thiemann /at/ uibk /dot/ ac /dot/ at)
Submission date: 2010-06-14
Abstract: We present an Isabelle formalization of abstract rewriting (see, e.g., the book by Baader and Nipkow). First, we define standard relations like joinability, meetability, conversion, etc. Then, we formalize important properties of abstract rewrite systems, e.g., confluence and strong normalization. Our main concern is on strong normalization, since this formalization is the basis of CeTA (which is mainly about strong normalization of term rewrite systems). Hence lemmas involving strong normalization constitute by far the biggest part of this theory. One of those is Newman's lemma.
Change history: [2010-09-17]: Added theories defining several (ordered) semirings related to strong normalization and giving some standard instances.
[2013-10-16]: Generalized delta-orders from rationals to Archimedean fields.
  author  = {Christian Sternagel and René Thiemann},
  title   = {Abstract Rewriting},
  journal = {Archive of Formal Proofs},
  month   = jun,
  year    = 2010,
  note    = {\url{https://isa-afp.org/entries/Abstract-Rewriting.html},
            Formal proof development},
  ISSN    = {2150-914x},
License: GNU Lesser General Public License (LGPL)
Depends on: Regular-Sets
Used by: Decreasing-Diagrams, Decreasing-Diagrams-II, First_Order_Terms, Matrix, Minsky_Machines, Myhill-Nerode, Polynomial_Factorization, Polynomials, Rewriting_Z, Well_Quasi_Orders